In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

In [1], Atar and Zeitouni established an exponential asymptotic (in t → ∞) rate of convergence for the distance between differently initialized filter outputs when a signal is Markov process valued in a finite state space for both the discrete and continuous time cases (see related topic in [2]). In this note, we discuss only continuous time case1 and deal with exponential stability of the Wonh...

The following lemma is implied by Theorem 1 in Abbasi-Yadkori et al. (2011): Lemma 7. (Abbasi-Yadkori et al., 2011) Let (F ′ t; t ≥ 0) be a filtration, (mt; t ≥ 1) be an R-valued stochastic process such that mt is (F ′ t−1)-measurable, (ηt; t ≥ 1) be a real-valued martingale difference process such that ηt is (F ′ t)-measurable. For t ≥ 0, define ξt = ∑t τ=1mτητ and Mt = Id + ∑t τ=1mτm T τ , wh...

For any α-stable Lévy process with jumps on both sides, where α ∈ (1, 2), we find the Mellin transform of the first hitting time of the origin and give an expression for its density. This complements existing work in the symmetric case and the spectrally one-sided case; cf. [38, 19] and [33, 36], respectively. We appeal to the Lamperti– Kiu representation of Chaumont et al. [16] for real-valued...

Abstract We extend to matrix-valued stochastic processes, some well-known relations between realvalued diffusions and classical orthogonal polynomials, along with some recent results about Lévy processes and martingale polynomials. In particular, joint semigroup densities of the eigenvalue processes of the generalized matrix-valued Ornstein-Uhlenbeck and squared OrnsteinUhlenbeck processes are ...

Let G be a Galton-Watson tree, and for 0 u 1 let Gu be the subtree of G obtained by retaining each edge with probability u. We study the tree-valued Markov process (Gu; 0 u 1) and an analogous process (G u; 0 u 1) in which G 1 is a critical or subcritical Galton-Watson tree conditioned to be in nite. Results simplify and are further developed in the special case of Poisson( ) o spring distribut...

In this paper, we present structure of the fixed point set results for condensing set-valued map. Also, we prove a generalization of the Krasnosel'skii-Perov connectedness principle to the case of condensing set-valued maps.

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...